Matrix product states and the nonabelian rotor model

Abstract

We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for $U(1)$ and $SU(2)$, respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the $\beta$ function, we find excellent agreement with known results, locating the BKT transition for $O(2)$ and successfully entering the asymptotic weak-coupling regime for $O(4)$. To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the nonabelian theory, where entanglement also suddenly increases. This could have important consequences for TNS studies of Yang-Mills on higher dimensional graphs.

Comments: 6 pages, 4 figures. Code at https://github.com/amilsted/mps-rotors